Have a personal or library account? Click to login

Best possible estimates of weak solutions of boundary value problems for quasi-linear elliptic equations in unbounded domains

Open Access
|Sep 2017

References

  1. [1] Borsuk, M.V.: Transmission problems for elliptic second-order equations in non-smooth domains. Birkhäuser Basel book (2010)10.1007/978-3-0346-0477-2
  2. [2] Borsuk, M.V., Wiśniewski, D.: Boundary value problems for quasilinear elliptic second order equations in unbounded cone-like domains, Cent.Eur.J.Math., (2012), 2051-207210.2478/s11533-012-0127-2
  3. [3] Cirmi, G.R., Porzio, M.M.: L1 - solutions for some nonlinear degenerate elliptic and parabolic equations, Ann. mat. pura ed appl. (IV) 169 (1995), 67-8610.1007/BF01759349
  4. [4] Drabek, P., Kufner, A., Nicolosi, F.: Quasilinear elliptic equations with degenerations and singularities. Walter de Gruyter. Berlin, NY, 199710.1515/9783110804775
  5. [5] Furusho, Ya.: Existence of global positive solutions of quasilinear elliptic equations in unbounded domains, Funkcialaj Ekvacioj, 32 (1989), 227-242
  6. [6] Hernández, J., Mancebo, F.J., Vega, J.M.: On the linearization of some singular, nonlinear elliptic problems and applications, Ann. Inst. H. Poincar_e Anal.Non Lin_eaire 19 (2002), 777-813.10.1016/s0294-1449(02)00102-6
  7. [7] Kondratiev, V., Liskevich, V., Moroz, V.: Positive solutions to superlinear second-order divergence type elliptic equations in cone-like domains, Ann. Inst. H. Poincare Anal. Non Lineaire, 22 (2005), 25-43.10.1016/j.anihpc.2004.03.003
  8. [8] Lazer, A.C., McKenna, P.J.: On a singular nonlinear elliptic boundaryvalue problem, Proc. Amer. Math. Soc. 111 (1991), 721-730.10.1090/S0002-9939-1991-1037213-9
  9. [9] Mityushev, V., Adler, P.: Darcy ow around a two-dimensional lens, I. Phys. A: Math. Gen. 39, 2006, 3545-3560.10.1088/0305-4470/39/14/004
  10. [10] Murray, J.D.: Mathematical Biology, Springer, Berlin (1993).10.1007/978-3-662-08542-4
  11. [11] Murthy, M.K.V., Stampacchia, G.: Boundary value problem for some degenerate elliptic operators, Ann. Math. Pura Appl. 80 (Ser. IV) (1968)10.1007/BF02413623
  12. [12] Nachman, A., Callegari, A.: A nonlinear singular boundary value problem in the theory of pseudoplastic uids, SIAM J. Appl. Math. 38(1980), 275-281.10.1137/0138024
  13. [13] Noussair, E.S., Swanson, C.A.: Decaying entire solutions of quasilinear elliptic equations, Funkcialaj Ekvacioj, 31 (1988), 415-438
  14. [14] Okubo, A., Levin, S.A.: Di_usion and Ecological Problems: Modern Prospectives, Springer, New York (2001).10.1007/978-1-4757-4978-6
  15. [15] Ouassarah, A.A., Hajjaj, A.: Existence of solutions for quasilinear elliptic boundary value problems in unbounded domains, Bull. Belg. Math. Soc. 3 (1996), 217-225.10.36045/bbms/1105540794
  16. [16] Pao, C.V.: Nonlinear elliptic boundary-value problems in unbounded domains, Nonlinear Analysis, Theory, Methods and Applications, Vol. 18, No. 8 (1992), 759-77410.1016/0362-546X(92)90170-J
  17. [17] Shilov, G.E., Gel'fand, I.M.: Generalized functions, 1964, v. I. Academic Press
  18. [18] Wiśniewski, D.: Boundary value problems for a second-order elliptic equation in unbounded domains, Ann. Univ. Paed. Cracov. Studia Math. IX (2010)
DOI: https://doi.org/10.1515/auom-2017-0030 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 201 - 224
Submitted on: Mar 9, 2016
Accepted on: Jul 5, 2016
Published on: Sep 21, 2017
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 times per year

© 2017 Damian Wiśniewski, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.